Hey Alex:
Consistent with my experience, the WolframAlpha dev support team has resolved this issue that I reported. The fix is:
WolframAlpha["all visible satellites"
, {{"VisibleNonDebrisSatellitesAtDatFromLocation", 1}
, "ComputableData"}]
Indeed all 700 satellites (at my location) are enumerated.
A nice touch is that when you do this query on the W|a site, the satellite names are "hot" where selection brings up a display showing the path through the sky.
Regards..